Problem: $f(x) = -5x-2$ $g(t) = -t^{2}-2(f(t))$ $h(x) = 4x^{2}-7x+2-3(g(x))$ $ f(h(2)) = {?} $
Solution: First, let's solve for the value of the inner function, $h(2)$ . Then we'll know what to plug into the outer function. $h(2) = 4(2^{2})+(-7)(2)+2-3(g(2))$ To solve for the value of $h$ , we need to solve for the value of $g(2)$ $g(2) = -2^{2}-2(f(2))$ To solve for the value of $g$ , we need to solve for the value of $f(2)$ $f(2) = (-5)(2)-2$ $f(2) = -12$ That means $g(2) = -2^{2}+(-2)(-12)$ $g(2) = 20$ That means $h(2) = 4(2^{2})+(-7)(2)+2+(-3)(20)$ $h(2) = -56$ Now we know that $h(2) = -56$ . Let's solve for $f(h(2))$ , which is $f(-56)$ $f(-56) = (-5)(-56)-2$ $f(-56) = 278$